Search

Over the past decades, tremendous effort has gone into building a universal quantum computer. In theory, such a device can solve certain problems such as factoring exponentially faster than digital computers. The leading technological prototypes are based on superconducting circuits and contain about 10-50 qubits. Controlling these fragile systems requires an enormous amount of precision, posing a difficult challenge for the experimentalists. We study such quantum systems in detail by solving the time-dependent Schrödinger equation for a generic model Hamiltonian. For this purpose, we have developed efficient product-formula algorithms that are tailored to key features of the model Hamiltonian. This allows us to simulate each individual voltage pulse that is used in experiments to realize a certain quantum gate, as dictated by the computational model of a quantum computer. By optimizing the pulse parameters, we find that even in the ideal case, the best pulses still contain undesirable errors in the realization of the intended quantum gate. The common gate metrics measured and reported in experiments or computed in theory are shown to provide insufficient practical information about the significance of these errors.

Over the last decades, tremendous effort has gone into building a universal quantum computer. In theory, such a device can solve certain problems such as factoring exponentially faster than digital computers. The leading technological prototypes are based on superconducting circuits and comprise up to 17 qubits. Controlling these fragile systems requires an enormous amount of precision, posing a difficult challenge for the experimentalists. We study such quantum systems in detail by solving the time-dependent Schrödinger equation for a generic model Hamiltonian. For this purpose, we have developed efficient product-formula algorithms that are tailored to key features of the model Hamiltonian. This allows us to simulate every individual controlling pulse that is used in experiments to realize a certain quantum gate, as dictated by the computational model of a quantum computer. By optimizing the pulse parameters, we find that even in the ideal case, the best pulses still contain undesirable errors in the realization of the intended quantum gate. The common gate metrics measured and reported in experiments or computed in theory are shown to provide insufficient practical information about the significance of these errors.

For quantum computers, there are two theoretical models which are nowadays considered to be the most important: the gate-based quantum computer and the quantum annealer.Gate-based quantum computers are based on computational gates just like classical computers are, but have potentially more computational power due to the algebra behind quantum theory. A quantum annealer works fundamentally different: First the system is prepared in a known ground state of an initial Hamiltonian, then this Hamiltonian is adiabatically transformed into the final Hamiltonian whose ground state corresponds to the solution of a given problem, usually taken from the class of optimization problems.Quantum annealing works well in theory if the qubits can be described by two-level systems. However, in real devices qubits are not based on a perfect two-level system, but on a two-dimensional subspace of a larger system. This makes approximations in analytic calculations unavoidable.With a simulation utilizing the Suzuki-Trotter product-formula approach for solving the time-dependent Schrödinger equation, the time-evolution of the full state of such a device based on superconducting flux qubits is investigated.